Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 634 · 40 questions

How to solve it (Name the topic, then solve): Name the topic first: angles, counting, worst case, probability, digits, mensuration, data, coordinates, AP, algebra, primes or Venn diagrams. Use that lesson’s method; draw a quick sketch, list or Venn diagram on rough paper. Rule out options of the wrong kind — a probability above 1, or a triangle angle of 180° or more. Check by working backwards or with a second method when you can.

1. 1.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 693 sq cm
2. 2.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 1/6 (b) 7/36 (c) 6/11 (d) 1/11
3. 3.A canteen sells 3 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 9 (c) 6 (d) 18
4. 4.Which is the correct factorisation of x² + 13x + 42? (a) (x + 1)(x + 42) (b) (x + 6)(x + 7) (c) (x − 6)(x − 7) (d) (x + 1)(x + 12)
5. 5.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 49 (c) 42 (d) 21
6. 6.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
7. 7.In a class of 42 children, 17 like maths, 18 like science and 3 like both. How many like only maths? (a) 14 (b) 24 (c) 15 (d) 17
8. 8.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 20 (c) 15 (d) 10
9. 9.What is the smallest prime factor of 221? (a) 2 (b) 1 (c) 13 (d) 17
10. 10.In a league, 7 teams each play every other team once. How many matches are played? (a) 21 (b) 49 (c) 42 (d) 28
11. 11.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 100 (b) 90 (c) 45 (d) 55
12. 12.In a league, 14 teams each play every other team once. How many matches are played? (a) 91 (b) 105 (c) 196 (d) 182
13. 13.In which quadrant does the point (−4, −2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
14. 14.What is the 10th term of the AP 2, 5, 8, 11, …? (a) 27 (b) 29 (c) 30 (d) 32
15. 15.The mean of 4 numbers is 16. When the number 31 is added to them, what is the new mean? (a) 20 (b) 18 (c) 16 (d) 19
16. 16.A bag has 6 green balls and 5 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 7 (b) 11 (c) 2 (d) 8
17. 17.What is the midpoint of the line joining (6, 4) and (8, 8)? (a) (14, 12) (b) (6, 7) (c) (7, 6) (d) (1, 2)
18. 18.What is the midpoint of the line joining (5, 14) and (15, 10)? (a) (12, 10) (b) (5, 2) (c) (10, 12) (d) (20, 24)
19. 19.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 130° (b) 155° (c) 25° (d) 310°
20. 20.A bag has 4 green, 6 yellow and 8 blue balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 1/3 (b) 2/3 (c) 7/18 (d) 1/2
21. 21.A cuboid is 12 cm long, 5 cm wide and 9 cm high. What is its volume? (a) 26 cu cm (b) 60 cu cm (c) 540 cu cm (d) 426 cu cm
22. 22.A cube has edges of 7 cm. What is its total surface area? (a) 294 sq cm (b) 49 sq cm (c) 196 sq cm (d) 343 sq cm
23. 23.How many factors does 99 have? (a) 6 (b) 5 (c) 7 (d) 4
24. 24.Two angles of a triangle are 60° and 40°. What is the exterior angle at the third corner? (a) 100° (b) 120° (c) 80° (d) 140°
25. 25.What is the 33rd term of the AP 12, 21, 30, 39, …? (a) 300 (b) 288 (c) 309 (d) 297
26. 26.What is the midpoint of the line joining (2, 2) and (6, 10)? (a) (8, 12) (b) (4, 6) (c) (2, 4) (d) (6, 4)
27. 27.A bag has 9 yellow balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 10 (b) 12 (c) 2 (d) 11
28. 28.Two angles of a triangle are 45° and 70°. What is the third angle? (a) 115° (b) 110° (c) 65° (d) 135°
29. 29.3 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 5 (b) 9 (c) 12 (d) 6
30. 30.Two angles of a triangle are 80° and 70°. What is the third angle? (a) 110° (b) 30° (c) 150° (d) 100°
31. 31.Two angles of a triangle are 55° and 70°. What is the third angle? (a) 110° (b) 55° (c) 125° (d) 235°
32. 32.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 55° (c) 35° (d) 145°
33. 33.What is the smallest prime factor of 155? (a) 1 (b) 31 (c) 5 (d) 2
34. 34.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 155° (b) 25° (c) 65° (d) 335°
35. 35.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 22 (b) 21 (c) 28 (d) 29
36. 36.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 88 sq cm (d) 616 sq cm
37. 37.The mean of 5 numbers is 13. When the number 1 is added to them, what is the new mean? (a) 13 (b) 11 (c) 7 (d) 12
38. 38.What is the sum of the roots of x² − 14x + 48 = 0? (a) 14 (b) 48 (c) 15 (d) 13
39. 39.How many prime numbers are there between 90 and 100? (a) 0 (b) 3 (c) 2 (d) 1
40. 40.A bag has 6 green, 4 red and 3 white balls. One ball is taken out without looking. What is the probability that it is green? (a) 7/13 (b) 1/3 (c) 6/13 (d) 6/7

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